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Q.11
The quotient of
𝑎
is an odd integer and there is no remainder. Which must be the correct
7
statement from below?
A.
B.
C.
D.
E.
a is a prime integer
a is consecutive integer
a is an even integer
a is an odd integer
a is multiple of 3
Solution;
The odd integers are 1, 3, 5, 7………………….
Here it is given that the quotient of
𝑎
If
7
𝑎
7
𝑎
7
𝑎
7
is an odd integer that means
= 1; then a = 7
= 3; then a = 21
= 5; then a = 35
That means for any value of
𝑎
7
to be odd the value of ‘a’ must be odd. So the correct answer
choice is ‘D’.
Q.12
What are the multiple of 3, 6, & 9? Choose all the options from the following.
A.
B.
C.
D.
E.
12
15
18
36
54
Solution;
If we check option choice one by one we can easily get the answer.
A.
B.
C.
D.
E.
12 = Multiple of 3 and 6
15 = Multiple of 3
18 = Multiple of 3, 6 and 9
36 = Multiple of 3, 6 and 9
54 = Multiple of 3, 6 and 9
So, correct answer will be C, D
Q.13
and E.
m is an even integer and n is an odd integer
Quantity A
Quantity B
m
3
n
A. If Quantity A is greater
B. If Quantity B is greater
C. If Quantity A and Quantity B are equal
D. The relationship cannot be determined from given information
Solution;
Let us take values for m and n
If m = 2, n = 1 then m/n = 2/1 = 2 Quantity A is greater
If m = 12, n =3 then m/n = 12/3 = 4 Quantity B is greater
So, Both the Quantity A & Quantity B cannot be compared from given data, Hence
Answer is ‘D’.
Q.14
Dividend ‘x’ = 36. ‘x’ is square of its quotient
Quantity A
Quantity B
Divisor of ‘x’
6
A. If Quantity A is greater
B. If Quantity B is greater
C. If Quantity A and Quantity B are equal
D. The relationship cannot be determined from given information
Solution;
Here it is given that Dividend = x = 36, which is square of its quotient. That means 36 is square
of its quotient which should be ‘6’. So if we divide 36 with 6 then only ‘x’ can be square of
quotient.
So in above condition;
Dividend = x = 36
Divisor = 6
Quotient = 6
The value for Quantity A will be 6. Now if we compare The value of Quantity B which is also 6 ,
it comes out equal so correct answer choice will be ‘C’.
Q.15
The integer m is even and integer n is even and prime. The square of ‘m’ is addition of m and n.
Find the least possible value for ‘m’?
Solution;
The possible values for ‘m’ could be 2, 4, 6, 8………………………..
The value for ‘n’ will be = 2, as 2 is only even and prime number.
Now if we take ‘m’ = 2, ‘n’ = 2, then m2 = m x m = 2 x 2 = 4
Now addition of
m + n = 2 + 2 = 4.
As the least possible value is being asked, so this condition justifies the asked question.
So the least possible value for ‘m’ will be =2.
Q.16 If ‘x’ is double to the next number of sum of first three prime numbers.
Quantity A
Quantity B
x
23
A. If Quantity A is greater
B. If Quantity B is greater
C. If Quantity A and Quantity B are equal
D. The relationship cannot be determined from given information
Solution;
The first three prime numbers are 2, 3 and 5
The Sum = 2 + 3 + 5 = 10
Next number to 10 is 11.
Double of 11, so ‘x’ = 2 x 11 = 22
If we compare Quantity A = x = 22 and Quantity B = 23, Quantity B is always greater.
The correct answer choice is ‘B’.
Q.17 If ‘x’ is even and prime. It is one of the factors and digit at ten’s place of the number of
another factor with a digit at one’s place is square of 3. What is that number?
Solution;
‘x’ is even and prime i.e. x = 2 , Now there is one integer with two factors .
One of the factors is 2. And for second factor it is given that digit at tens place is 2 and one’s
place is square of 3 which is 9. So, the second factor is 29.
Hence the number = 2 x 29 = 58.
The correct answer is 58.
Q. 18
If ‘m’ is a positive integer and ‘n’ is a negative integer then which of the following value must be
true for m - n?
A.
B.
C.
D.
E.
Positive
Negative
Positive and even
Prime
Only even
Solution;
Let us take the positive value for (i) m = 1 and negative value for n = -1;
Then m-n = 1 – (-1) = 1 + 1 = 2
(ii) Now take next value for m = 3 and n = -5
Then m-n = 3 – (-5) = 3 + 5 = 8
(iii) For m = 5 and n = -4
Then m – n = 5 – (- 4) = 5 + 4 = 9
(iv)Take one more value for m = 6 and n= -8
Then m – n = 6 – (- 8) = 6 + 8 =14
Every time the result is positive integer only.
So correct answer is ‘A’.
Q. 19 If ‘m’ is multiplied to ‘n’ the result is 1. If ‘m’ is divided by ‘n’ the result is 4 what is m +
n?
A.
B.
C.
D.
E.
1
5
3
4
5
6
1
2
5
2
Solution;
m x n = 1 …………………………….Equation 1
m
n
= 4 so, m = 4n ……………………. Equation 2
Now put value of ‘m’ in equation 1
4n x n = 1
n2 =
1
4
;
Taking square root both side;
n=
𝟏
√𝟒
=
𝟏
𝟐
𝟏
m = 4n = 4 x 𝟐
=2
Therefore, m + n = 2 +
𝟏
𝟐
=
𝟓
𝟐
The correct answer choice is ‘E’.
Q.20 If a is square of integer t
Quantity A
Quantity B
a
t
t
a
A. If Quantity A is greater
B. If Quantity B is greater
C. If Quantity A and Quantity B are equal
D. The relationship cannot be determined from given information
Solution;
The best rule to solve this problem is taking one positive and one negative value for given
variables and compare the Quantity A with Quantity B.
Let us start by putting the values for integer‘t’.
If t = 2 then a = 22 = 2 x 2 = 4
(i)
a
t
=
4
2
t
=2
a
=
2
4
=
1
2
= 0.5
Quantity A is greater, Eliminate Choice ‘C’
If t = -3 then a = (-3)2 = 9
(ii)
a
t
=
9
−3
= -3
Quantity B is greater
t
a
=
−
3
9
= - 0.33
As it is difficult to reach to any conclusion after comparing Quantity A and Quantity B, The
correct answer choice will be ‘D’.